Prime Gaps
number_theory · 36 views
number_theory
What It Is
Gaps between consecutive primes --- locally erratic but statistically governed by the prime number theorem, with conjectured connections to random matrix theory
Interpretation
Standard analysis sees: right-skewed; blue spectrum (high-frequency power); aperiodic / broadband. The atlas detects no named structure beyond this.
What standard analysis sees
tail heaviness0.84
asymmetry0.90
occupancy0.21
short-range corr0.18
long-range memory0.18
spectral colour0.86
periodicity0.08
complexity0.83
time-irreversibility0.61
volatility clustering0.18
multifractality0.37
dimensionality0.61
nonstationarity0.42
What the atlas adds
Nothing beyond the standard reading — this source’s structure is already captured by standard features; the atlas adds no named residual.
Composition
dtypefloat64
range[2, 132]
unique values48 / 16384
mean ± std14.3 ± 12
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Prime_Gaps.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Prime_Gaps.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Prime_Gaps.png)
Inflation (Substitution) > barcode
/d_curve/Prime_Gaps.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/Prime_Gaps.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/Prime_Gaps.png)
Ulam Spiral (Sacks) > default
/default/Prime_Gaps.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Geometric Waiting Times | 2.29 | cross-domain |
| Poisson Spacings | 2.72 | cross-domain |
| Zipf Distribution | 3.52 | cross-domain |
Which Geometries Light Up
Nonstationarity › Nonstationarity:trajectory_dim | rank 5/298 | 0.8142 |
Penrose (Quasicrystal) › Penrose (Quasicrystal):phi_tower | rank 296/298 | -1.7664 |
Zipf–Mandelbrot (16-bit) › Zipf–Mandelbrot (16-bit):zipf_r_squared | rank 3/298 | 0.9907 |
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